Physicists prefer to use hermitian operators, while mathematicians are not biased towards hermitian operators I've found lots of different proofs that so(n) is path connected, but i'm trying to understand one i found on stillwell's book naive lie theory What is the fundamental group of the special orthogonal group $so (n)$, $n>2$
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The answer usually given is
The generators of so(n) s o (n) are pure imaginary antisymmetric n×n n × n matrices
How can this fact be used to show that the dimension of so(n) s o (n) is n(n−1) 2 n (n 1) 2 I know that an antisymmetric matrix has n(n−1) 2 n (n 1) 2 degrees of freedom, but i can't take this idea any further in the demonstration of the proof To gain full voting privileges, I have known the data of $\\pi_m(so(n))$ from this table
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